MA131 Fall 2013
Section 06
Quiz 6 Hint
1. Solve the following problem.
Water is leaking out of an inverted conical tank at a rate of 11,500 cm3 /min
at the same time that water is being pumped into the tank at a constant
rate. The tank has height 6 m and the diameter at the top is 4 m. If the
water level is rising at a rate of 20 cm/min when the height of the water is 2
m, find the rate at which water is being pumped into the tank. (Round your
answer to the nearest integer.)
Hint:
We know that Vcone = 31 πr2 h. Thus
product rule.
dV
dt
=
π d(r2 h)
3 dt
=
π
dh
3 (2rh dt
+ r2 dr
dt ) with
In a cone, r is proportional to h, which means r = αh. From h = 6m and
1 dh
r = 2m, we can calculate α = 31 . Thus r = 13 h, and dr
dt = 3 dt .
Thus
dV
dt
2
can be written as π3 ( 2h3
dh
dt
+
h2 dh
9 dt ).
From the question, h is known here to be 2m and
and we can calculate dV
dt .
dh
dt
is known to be 20cm/min
We also notice that dV
dt = V olumeChangein − V olumeChangeout , where
V olumeChangeout is a known number of 11,500 cm3 /min. It will be easy
to calculate the volume out speed.
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